Question

The diameter of a sphere is increases by 25%. By what percent does its curved surface area increase?​

Answer 1

Given that, diameter of a sphere is increased by 25%

To find out: Percentage increase in the curved surface area (C.S.A.) of the sphere.

Let the initial diameter of the sphere be d.

Hence, increased diameter =d+25%×d

d+0.25d=1.25d

Hence, initial radius = d/2

and increased radius = 1.25d/2

We know that, curved surface area of a sphere =4πr²

∴ Initial C.S.A. =4π(d/2)² =πd²

and increased C.S.A. =4π(1.25d/2)² =π(1.25d)²

=(1.5625)πd²

We know that, % increase=

(increased−initial)/initial ×100

∴ % increase in C.S.A. = (1.5625πd²−πd²)/πd² ×100

= (1.5625−1)πd²/πd² ×100

=56.25%

Hence, the required percentage increase in C.S.A. is 56.25%.

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